Basketball Reference

Loading Data through Basketball Reference

Tidyverse

• tidyverse

install.packages("tidyverse", repos = "http://cran.us.r-project.org")

Package for Acquiring Data

• hoopR

if (!requireNamespace('devtools', quietly = TRUE)){
  install.packages('devtools')
}
devtools::install_github("sportsdataverse/sportsdataverse-R")

Package for Visualizing and Analyzing Data

• BasketballAnalyzeR

devtools::install_github("sndmrc/BasketballAnalyzeR")

Four Factors

Shot Chart

Assist Network

Expected Points

Expected value: \(y_i\) are all the possible values of a discrete variable \(Y\).

\(E(Y) = \sum_{i = 1}^n y_i P(Y = y_i)\)

Expected Points

Expected Points

Conditional expected value: let \(X\) be some variable that changes the probability of \(y_i\).

\(E(Y | X) = \sum_{i = 1}^n y_i P(Y = y_i | X)\).

Cluster Analysis

How many possible March Madness bracket outcomes are there?

The standard scoring of a bracket is

Round One: 1

Round Two: 2

Sweet Sixteen: 4

Elite Eight: 8

Final Four: 16

Championship: 32

A perfect bracket gets a score of 192.

Ranking by some metric

This could be as simple as using AP rankings, or you could develop your own metric. You can evaluate your metric based on how it performs on past tournaments.

Ranking by some metric

Example:

Ranking by some metric

• We can pick the best team at each stage
• Strict hierarchy is unrealistic and one prediction for a tournament has a lot of uncertainty

How do we model how good a team is?

We can predict the probability of a team winning a certain March Madness game.

What are some possible features?

“Probabilistic” approach

Depending on choice of model, it may be possible that the team most likely to advance at one stage may be less likely to advance at a future stage.

Example:

“Probabilistic” approach

• Can account for differences in playstyles
• Not practical to compute (9,223,372,036,854,775,808 different possibilities to consider)

How do we model how good a team is?

We can predict how many points a team will score in a March Madness game.

Regression works for continuous variables that have a support of \((-\infty, \infty)\), so we must use a link function to map the counts to real variables.

Poisson Regression

For regression, let \(Y\) be the number of points scored by the team of interest, and let \(x_j\) be the \(j\)th predictor out of \(n\).

Then \(\log(E(Y | x)) = \theta_0 + \theta_1x_1 + \theta_2x_2 + ... + \theta_nx_n\)

Simulation approach

For each team in a game, we can draw from Pois\((\lambda)\), where \(\lambda\) is the predicted response from our regression for that team’s points. The team that scores more points advances. We can simulate a tournament as many times as we want. Then we can get an idea of how likely a team is to make it to a certain round. Note that the most likely bracket may not coincide with the most likely winner.

Simulation approach

Simulation approach

• Doesn’t require as much processing
• Hard to find optimal bracket

Vibes Bracket

Pick the teams you think will win, or the teams you personally want to win. It worked great for UConn students! Just make sure you don’t pick too few or too many upsets.

Picking Upsets

NCAA Average Number of Upsets:

• Total Upsets: 8.5
• First Round: 4.65
• Second Round: 3.13
• Elite Eight: 0.31
• Final Four: 0.10

The End